Length-preserving monomorphisms for Steenrod algebras at odd primes
type: Item
instance of: scholarly article
title: Length-preserving monomorphisms for Steenrod algebras at odd primes
zbMATH Open document ID: 1407.55006
author: Maurizio Brunetti
author: A. Ciampella
published in: Bollettino dell'Unione Matematica Italiana
publication date: 2018-12-10T00:00:00Z
review text: In the present paper the authors consider endomorphisms of mod \(p\) Steenrod algebras (the ordinary one \(\mathcal A(p)\), and \(\mathcal B(p)\), the algebra of cohomology operations for the cohomology of cocommutative Hopf algebras over \(\mathbb F_p\)), where \(p\) is an odd prime. It is proved that every such monomorphism which preserves the length of the monomials must be an automorphism (a result which does not hold in the case \(p=2\)). The groups of these length-preserving automorphisms are also determined: \[ \underline{\mathrm{Aut}}(\mathcal A(p))\cong\mathbb Z_{p-1}\times\mathbb Z_{p-1}, \quad \underline{\mathrm{Aut}}(\mathcal B(p))\cong\mathbb Z_{p-1}\times\mathbb Z_{p-1}\times\mathbb Z_{p-1} \] (\(\mathbb Z_{p-1}\) is, as usual, the cyclic group of order \(p-1\)).
Mathematics Subject Classification ID: 55S10
Mathematics Subject Classification ID: 55S05
zbMATH DE Number: 6991208
zbMATH Keywords: Steenrod algebra
zbMATH Keywords: cohomology operations
zbMATH Keywords: Hopf algebras
reviewed by: Branislav Prvulović
MaRDI profile type: Publication
full work available at URL: s40574-017-0155-8
OpenAlex ID: W2783036100
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DOI: 10.1007/S40574-017-0155-8
description: scientific article; zbMATH DE number 6991208